Fatih Terim's side was leading 2-1 in Sunday's clash thanks to a double from Didier Drogba when Felipe Melo was given his marching orders in second-half stoppage time for a two-footed lunge on an Ramon Motta.
The former Juventus midfielder was soon escorted off the pitch and raised his jersey to the BJK faithful, who soon entered the field of play chanting songs in reference to this summer's anti-government protests across Turkey.
Other fans threw seats and other items onto the pitch, with the players promptly escorted back into their changing rooms.
According to reports, police soon clashed with the fans, using tear gas to try to disperse them.
Neither club has made a statement on the events, though Besiktas midfielder Manuel Fernandes took to Twitter to slam both Melo and referee Firat Aydinus.
"Firat Aydinus the real protagonist of this game. You should be ashamed of being so bad. And of course I couldn't forget Melo.... Has no respect for anyone and should be banned for a long time!!" he wrote.